It is difficult to be a single parent, but that is no reason not to do it. Good luck to you!
Yes, your friend is in a fortunate position financially and many people have an income lower than £1500/mo from which they need to pay all bills, mortgage, food, car and other expenses, so to have £1500/mo fun money is a very enviable position.
That said, she didn't sign up to do everything on her own, so she will have a lot of feelings of rejection, resentment and other emotions related to being left holding the baby. I feel that whatever your situation ends up being, you will know that it was the result of YOUR choices whereas she cannot say the same.
There are lots of things about being a single parent that it is impossible to fully understand until you are in that situation though. It is relentless and gruelling, and you will constantly be told that other people understand what it's like, but they really don't.
Weekends are lonely because most of your/your kid's friends are having "family time" with both parents. The housework is never done because there just aren't enough hours in the day compared to having one person putting the kids to bed while the other one tidies up. You may have to reduce your working hours to fit around childcare (income, career progression, pension pot all take a hit). When the kids are ill you have to take time off work and that isn't shared with another person (so work/career can suffer). You can't just pop out if you run out of milk - you have to take everyone to and around the shop. You can't see your friends as much because you have noone to watch the child(ren) and babysitters are expensive. If you are feeling rotten, you can't rest up in bed, you still have to get up and do everything. Everything takes a lot longer because it is only you doing it.
And yes, financially it is hard too. Not many single parents are able to find a job paying £50k for 3 days, and it is hard having to tell your children "no" when they want what their friends have or seeing all the extracurricular activities that their friends are able to do that are simply not affordable on (most) part-time wages.
But it is also very rewarding, and I am so, so glad I have my amazing, wonderful children in my life.